The invention relates to a method of determining the stroke volume and the cardiac output of the human heart from the pulse-type bloodstream pressure signal derived from the aorta and consisting in each case of a systolic and diastolic period. It is known in practice to calculate the stroke volume and the cardiac output with the aid of a thermodilution determination by injecting cold liquid into the blood stream and measuring it downstream at regular intervals.
In another known method, a pulse contour method or prescription is used to determine the stroke volume V.sub.s and the cardiac output or heart minute volume Q from a pressure signal p(t) measured in the human aorta. In this connection, the stroke volume is the volume of blood ejected by the heart in one contraction or stroke. A typical value is, for example, 70 cm.sup.3, but this quantity can vary from stroke to stroke. The cardiac output is the volume of blood which the heart pumps in a unit time of one minute. In this connection, a typical value is 5 l/min, and this volume can typically vary between 2 and 30 l/min.
In the past relatively simple relationships have been assumed between the measured aorta pressure signal p(t) and the mean aorta flow q(t). In this connection, the starting point is the pressure signal since said pressure can be measured relatively easily and well, but the flow cannot. In practice it has been found that such a relationship or "model" is much more complicated than was first assumed. This has emerged, in particular, in hospitals, where this so-called pulse contour calculation has resulted in frustration in the case of seriously ill patients.
In practice, usually a so-called "Windkessel" or air-receiver model is assumed, the aorta being conceived as a single compliance (FIG. 1b). In this case a windkessel--a container partially filled with liquid and with gas--which can absorb the surges in flow and buffer them in the gas bubble and which is incorporated downstream of a pulsatile pump is meant. The volume of blood ejected by the heart pump is largely received in the aorta or windkessel and partially flows away through the peripheral vascular regions of the various organs which branch off from the aorta. In the period in which the heart pump does not eject a volume of blood, i.e. the diastolic period T.sub.d, the outward flow from the windkessel continues to be fed to the peripheral vascular regions. The aorta does not then contain any gas but the aorta wall is elastic and this elastic vascular wall fulfils the same function as the windkessel.
This concept contains various factors which are neglected. Firstly, the aorta is much longer than wide. In fact, the pressure wave generated by the heart requires a time of 0.1 to 0.3 sec. to reach the end of the aorta and then approximately the same time to return to the heart, whereas the entire expulsion period of the heart (the systolic period or systole, T.sub.s) lasts only 0.2 to 0.4 sec. At the beginning of the output flow, only a small portion of the compliance is therefore available for buffering the outward flow. However, still more important is the fact that, after two times the propagation or transit time of the pressure wave, twice the capacity is available, albeit with a doubling of the initial pressure wave amplitude. In addition, a second neglect which is generally made is that the windkessel is linear, that is to say a doubling of the stored stroke volume is accompanied by a doubling of the pressure. In reality it has been known for a number of years from the work of G. J. Langewouters et al. in J. Biomechanics 17, pages 425-435 (1984) that the relationship between pressure p and volume V is strongly nonlinear in accordance with an arctangent function (FIG. 3a). In addition, said arctangent function is dependent on the age and sex of the patient. Finally, the drainage from the aorta to the peripheral vascular zones is not concentrated at one location but distributed along the aorta. That is to say, it takes a little time before the increased pressure at the start of the aorta has reached the various branching points to the peripheral vascular zones and the drainage actually increases due to the increased aorta pressure.
To summarise, the neglects therefore amount to the fact that the aorta does not behave linearly and that there is a time factor due to a travelling wave along the aorta.
In practice, however, another model is also assumed, the so-called transmission line model (FIG. 1a). In this approximation, the aorta is conceived as a homogeneous elastic tube of "adequate" length filled with liquid (blood), with drainage to the peripheral vascular zones concentrated at the end. Such a tube has two characteristic properties. A pressure wave generated by the heart at:the start of the tube travels at finite velocity v.sub.p to the end of the tube is partially reflected there and travels back to the start of the tube. By the time the reflected wave arrives there, the expulsion phase, the systole, of the heart is already over, the aorta valve is already closed and the heart no longer has any trouble from the reflected wave since the latter is, after all, held back by the closed valve. The "adequate length" is that length of tube which, given the propagation velocity of the wave, ensures that the reflected pressure wave does not return too soon. The propagation velocity v.sub.p is primarily determined by the area A of the cross section of the aorta, the compliance C' of the aorta per unit of length and the density .rho. of the blood in the tube as follows: ##EQU1##
In addition to the propagation velocity the second characterising property is the characteristic impedance Z.sub.0. This impedance reflects the ratio between the amplitude of the pressure wave and that of the accompanying flow wave in the aorta and is also affected by the cross sectional area A and the compliance C'. In fact, the characteristic impedance is given by the formula: ##EQU2##
The fact that the ratio between pressure p(t) and flow q(t) is fixed and given by the formula: q(t)=p(t)/Z.sub.0 means that the pressure wave and the flow wave at the start of the aorta are identical in shape at least till the instant that the reflected pressure (and flow) wave has (have) returned.
This model also contains various approximations which, although they have less serious consequences for the stroke volume calculation, make the latter still too inaccurate under certain circumstances. Firstly, it is also true of this model that the aorta does not behave linearly in relation to the relationship between pressure p and volume V and therefore, with constant aorta length, as regards the cross section A=V/1. Since the compliance C' per unit of length is the derivative of the area of the cross section with respect to pressure, at the prevailing pressure p.sub.0 : C'=[dA/dp]p.sub.0, A will indeed increase with increasing pressure, but at the same time C' will decrease because the aorta becomes increasingly less distensible with increasing pressure in accordance with the arctangent function mentioned (FIG. 3b). In a particular pressure region, these two factors will compensate for each other in the formula for Z.sub.0 and the latter will be virtually constant. At increasingly higher pressures, the decrease in C' takes place more quickly than the increase in A, and the characteristic impedance Z.sub.0 will start to slowly increase in accordance with the root of the inverse product of A and C'. The nonlinearity therefore plays a role but this is less serious than in the windkessel model. A second approximation is that the aorta is assumed to be homogeneous. In reality, the aorta is neither homogeneous in cross section nor in distensibility of the vascular wall. The aorta cross section decreases towards the periphery. This is initially compensated for because the arterial branches of the aorta start to contribute to the total cross section as soon as the pressure wave and flow wave reach the branches. In addition, the vascular wall is, however, increasingly less distensible towards the periphery. This manifests itself in a decrease in compliance C'. Since both A and C' in the formula for the characteristic impedance decrease over the aorta towards the periphery, Z.sub.0 will increase. This means that there is no question of a single reflection at the peripheral resistance at the end of the aorta tube, as assumed in the model, but that there are distributed reflections along the entire aorta, initially small but considerably increasing later in the systole. With a short systolic period, the heart only experiences the (low) impedance at the start of the aorta while contracting, but with a longer-lasting systole it also experiences the (higher) peripheral impedance. This will mean that the instantaneously expelled quantity of blood will become increasingly smaller as the systole advances since it is gradually curbed by the increasing reflected impedance.
A third approximation is the following. After the blood has been forced into the aorta due to an increase in the pressure, the pressure in the subsequent diastolic period will, of course, not be zero immediately, but the aorta will slowly empty through the peripheral resistance. As a consequence of this, the subsequent stroke will be forced out against a somewhat increased pressure and the two pressures will in fact be superimposed on each other. The diastolic pressure will always increase further with every stroke until equilibrium has been reached between systolic inward flow and diastolic outward flow. This is comparable to a windkessel function.
Finally, it is also true that the drainage is not concentrated at the end of the aorta but is distributed over the length thereof.
To summarise, the neglects are a consequence of the fact that the aorta has nonlinear properties and cannot be conceived as homogeneous.
Both the above model concepts are not adequate if an attempt is made to calculate the aorta flow pattern from the aorta pressure as a function of time during a systole using the models. The curve found with the transmission line model only resembles an actual flow curve to any extent under the conditions of a short -duration systole. The windkessel model does not actually even permit a calculation of a flow curve. In practice, for both models only the stroke volume of the heart, that is to say the flow curve integrated over one systole, is therefore calculated from the pressure curve.